Structural equation modeling reveals decoupling of ecological and self-perceived outcomes in a garden box social-ecological system

It is well known that green urban commons enhance mental and physical well-being and improve local biodiversity. We aim to investigate how these outcomes are related in an urban system and which variables are associated with better outcomes. We model the outcomes of an urban common—box gardening—by applying the Social-Ecological Systems (SES) framework. We expand the SES framework by analyzing it from the perspective of social evolution theory. The system was studied empirically through field inventories and questionnaires and modeled quantitatively by Structural Equation Modeling (SEM). This method offers powerful statistical models of complex social-ecological systems. Our results show that objectively evaluated ecological outcomes and self-perceived outcomes are decoupled: gardening groups that successfully govern the natural resource ecologically do not necessarily report many social, ecological, or individual benefits, and vice versa. Social capital, box location, gardener concerns, and starting year influenced the changes in the outcomes. In addition, the positive association of frequent interactions with higher self-perceived outcomes, and lack of such association with relatedness of group members suggests that reciprocity rather than kin selection explains cooperation. Our findings exemplify the importance of understanding natural resource systems at a very low “grassroot” level.

(1) Is the self-perceived outcome associated with the ecological outcome in the urban garden box system? While outcomes are typically divided into socio-economic and ecological outcomes 18 , here we expect the outcomes to be positively correlated. In this system, the livelihood importance is assumed to be low, but the other benefits are diverse 27 , and therefore, we conceptualize the socio-economic part of the outcomes as the multiple benefits known to be relevant for box gardening. It contains 12 different self-assessed benefits, including benefits related to the cultivations (create biodiversity, self-sufficiency, beautify the area, and fresh vegetables), which are in this case assumed to be positively related with producing good-quality and diverse harvest i.e. ecological outcome 36 . Ecological outcome represents diversely the objectively evaluated aspects of gardening success. In this way, we are also able to investigate if self-assessed ecological outcomes differ from the objectively evaluated ecological outcomes. (2) Which aspects of the SES framework subsystems (actors, governance and resource) are associated with changes in the outcomes in the urban garden box system? Our selection of variables into the study is based on the original framework of Ostrom 2,3 and prior knowledge on urban gardening [37][38][39] . We expect a positive association between outcomes and variables related to the resource due to higher resource amount (box number), higher motivation and knowledge (effort), higher productivity (shade), and lower risks outside  36,38,[40][41][42] . We expect the variables from the governance sub-system to have a positive influence on outcomes due to higher motivation and shared strategy (rules), trust in everyone`s participation and shared knowledge (involvement) 2,36,43,44 . Variables related to the actors are expected to have a positive effect on outcomes due to social benefits and aggregate contributions (group size, others number), reciprocity and trust (social capital), and a negative effect due to higher cost of self-organizing (group size), lack of knowledge and experience (starting year), negative experiences (damage) and lack of control on the resource state (worries) 2,3,41,43,44 (for more details consult Table 1). The variables have not been studied jointly before in this context and therefore we have no clear prediction on how their interrelations will influence the results. (3) What, if any, is the importance of the variables derived from evolutionary theories in the urban garden box system? We expect that stable gardening groups that are composed of relatives, where individuals interact more frequently with each other are more successful in creating positive outcomes due to kin selection, reciprocity and efficiency 4,22 . We examine the variables in a separate subsystem in order to compare the evolutionary explanations for cooperation and increase dialogue between evolutionary biology and SES theory.
To examine these questions, we adhere to Structural Equation Modeling (SEM) 45 that allows the construction of unobserved latent variables for the scientific constructs of interest (for a flowchart of the research activities see Fig. 2). The few occasions SEM has been used successfully when studying SESs support the method`s applicability 46,47 . First, we perform a confirmatory factor analysis (CFA) to evaluate whether the proposed two latent factors, i.e. self-perceived and ecological outcomes, can be reliably measured by the specific indicator variables recorded here, and whether these two are associated. The outcomes by definition consist of several aspects 3 and can be measured differently depending on the context 18 . Their modelling as latent variables enables us to include multiple measures of scientific constructs in one model and increase our understanding of the relative importance of these different measures. Second, we construct a full SEM to explore which variables belonging to the different SES framework and evolutionary theory subsystems are associated with the self-perceived and ecological outcomes (Fig.1).

Results
Garden boxes in Turku. In 2019 there were 664 garden boxes in 228 different locations in the urban area of the city of Turku. We collected data from two sources, field inventories and questionnaires, and combined them for the analyses resulting in a sample size of 121 gardener locations. All the variables used in the analyses, with a full description and expected associations, are found in Table 1. Measurement model for ecological and self-perceived outcomes. First, we applied CFA to construct a measurement model with ecological and self-perceived outcomes as latent variables. The latent variables were correctly measured by their indicators (Fig. 3). We investigated how well the model fits the observed data by a global fit of the model 48 . The models can be over-rejected due to our relatively small sample size, and we used Swain`s correction factor (in this study = 0.965) to correct the model fit indices. The Swain corrected global fit of the CFA model to the data was acceptable (chi-square value = 35.070, df = 26, p value = 0.110, RMSEA = 0.056, RMSEA 90 % C.I. = 0.000 / 0.099, CFI = 0.946). All the indicators had significant loadings onto their latent variables (p value < 0.005).
A more positive ecological outcome was associated with an increase in species number, economic value, quality, number and area of cultivations, and a decrease in weeds (Fig. 3). A more positive self-perceived outcome was associated with an increase in social, individual and ecological benefits (Fig. 3). The standardized factor loadings indicate that the most important indicators for the ecological outcome were species number, economic value and area of the cultivations, respectively. For the self-perceived outcome, the self-perceived ecological benefits had the highest, individual benefits the second-highest, and social benefits the lowest standardized factor loading.

Figure 1.
A simplified schematic diagram of the social-ecological system (SES) framework applied for urban gardening system in this study 3 . Sub-systems Actors, Governance, Resource and Evolutionary theory may influence the Outcomes, which itself is composed of Self-perceived and Ecological outcomes. The Self-perceived and Ecological outcomes may or may not be associated with each other in this system. To facilitate dialogue between evolutionary biology and SES literature and combine variables from somewhere between actors and governance, we treat Evolutionary theory as a subsystem.

SES framework and evolutionary subsystems of importance in urban garden boxes. The SEM
investigated if variables belonging to the actors, resource, governance, or evolutionary theory subsystems were associated with self-perceived and/or ecological outcomes (Fig. 4, Table 2). In the model, the global model fit indices are not available due to multiple imputation method to handle missing values (see methods 49 ). However, the aspects indicating reliable estimates are met, namely model convergence and small standard errors 50 . Starting year, a variable belonging to the actors subsystem, associated positively with both of the outcome latent variables, meaning that their values increased when box gardening was more recently started. Social capital (actors subsystem) associated positively with self-perceived outcome. Worries (actors subsystem) was negatively associated with self-perceived outcome. If people had answered they were considerably worried if something would happen to their cultivations over summer, the less outcome was obtained. Group meetings, a variable belonging to the evolutionary theory subsystem, associated positively with self-perceived outcomes. When the group interacted more frequently, the outcome was higher. Shade from the resource subsystem associated positively with the self-perceived outcome. If the group`s boxes were located in a sunnier spot, the outcome was higher. Some other predictors belonging to the concept actors were quite close to significant ( Table 2). Larger groups obtained more self-perceived outcome (group size: p value = 0.063) and a respondent who reported damage obtained more self-perceived (damage: p-value 0.085) as well as ecological (damage: p value = 0.090) outcome. The variance explained for the ecological outcome latent variable was modest, 36.3% (S.E. = 11.2%, p value = 0.001), but the SE model explained the variance in the self-perceived outcome latent variable well, 84.8% (S.E. = 10.7%, p value < 0.001).

Discussion
We apply the SES framework and evolutionary theory in a novel way to gain insight into the governance of urban garden boxes by self-organized gardening groups in the city of Turku in Finland. We find that (1) self-perceived and ecological outcomes in this urban gardening system are not associated. Against expectations 26,27,33 , gardeners who succeed in terms of ecological outcomes, i.e. good quality produce and species diversity do not necessarily self-evaluate to have succeeded ecologically, socially, and individually. We also find that (2) particular characteristics of the gardening group (starting year, worries and social capital) are associated with changes in the outcomes (especially self-perceived) in urban gardening. In contrast, few of the aspects related to governance system and resource associate with the outcomes. In addition, (3) we find that relatedness between resource users, a potential evolutionary explanation for cooperation, was not relevant in our case. However, repetition of interactions   Table S5 online for p-values and standard errors for each estimate). The error terms for the reflective indicators are shown after the arrows pointing to the indicators and they signify the variance not explained by the respective latent variable they are loading onto.
indeed positively influences the self-perceived outcomes of urban gardening, suggesting that reciprocity is more important than kin selection in this context. We first examined whether the multiple observed variables included in the study adequately measured selfperceived and ecological outcomes in the urban garden box resource system. The SES case studies rarely include more than one measure at a time, even though research would benefit from including multiple references 36,43,51 . Several measures describe more genuinely the multidimensional and complex reality of natural resource systems. Our model fitted the data satisfactorily and all our measured variables had significant loadings onto their latent variable. In urban gardening research the typical ecological performance measure is either the species diversity or the gardeners` evaluation of their harvest, which simplifies the numerous aspects related to the harvest or yield 32,37,43 . Socio-economic performance has been measured for example, by self-organization, livelihood, gender equity or different socioeconomic factors 18,34,36 . As the outcome measures are so various we encourage future studies of urban commons to include multiple measures of outcomes or benefits to arrive at a more holistic understanding of the system 51 .
The SEM approach offers sound statistical benefits when using many indicator variables to describe a latent, because it accounts for the measurement error, thereby providing more realistic estimates and acknowledging the difficulty in measuring the outcomes exhaustively 45 . Therefore, the conclusions based on latent variables are more general. When considering SES research, different studies can measure and compare the same concepts but operationalize them differently depending on the data and study aims. Lastly, SEM approach allows investigating the relative importance of different measures for the outcomes. Considering our latent variables, ecological benefits (to create biodiversity, self-sufficiency, to beautify the area, fresh vegetables) was the most important measure for the self-perceived outcome and species diversity was the most important measure for the ecological outcome. Against expectations, ecological and self-perceived outcomes did not correlate significantly 27,32 . Therefore, independently of the gardening success, the gardener can report to receive e.g. much or little quality time with friends and family, mental relaxation, and fresh vegetables. It seems that the importance of the physical resource is lower than expected 43 and the immediate human needs in this case might be fulfilled even when the ecological outcome is low. The importance of the resource for livelihood has been found to increase its sustainability 36 , which can partly explain the loss of connection here. The relationship between social and ecological aspects in social-ecological systems is complex and studies have found both positive, negative and no correlations between outcome variables 36,40,51 . As we were able to evaluate objectively the ecological outcome and compare it to the self-perceived one, our findings imply that people governing an urban common might consider they have reached satisfactory ecological benefits even though in reality this is not the case. However, our study sample is small and further work is needed to confirm if similar dynamics exist in other natural resource systems.
Interestingly, the self-evaluated ecological benefits were found to best measure the self-perceived outcome while still being uncorrelated with the ecological outcome. This contradiction suggests the need to strengthen the link between the local biodiversity outcomes and people`s perception of them when designing urban commons governance. Local species diversity is found to be connected to the ecological resilience in cities, which is one www.nature.com/scientificreports/ of the main goals of the gardening projects 12 . Based on our results, we can recommend that when the ecological outcomes are monitored in practice, it should not only happen through self-evaluation. Previous studies indicate that gardener motivations and knowledge influence e.g. the species diversity and therefore information considering these aspects should be available for gardeners to improve ecological outcomes 32,38 . The complex relationship between the outcomes points out the unfortunate (but not unexpected) fact that the immediate human needs often differ from sustainable ecological conditions 1 .
We demonstrate that SEM can be used to localize what are the most important variables associated with changes in outcomes in an urban garden box system. However, to maintain our sample size, we performed multiple imputations, which prevents us to study global fit indices for the model. First, against our expectations, members in gardening groups that started a longer time ago (starting year) reach less self-perceived as well as ecological outcomes. Previously it has been found that the gardening experience increases the total yield 52 and we assumed that the knowledge gained through gardening years would have a positive influence on outcomes 3,41 but, perhaps, the enthusiasm of starting a new "hobby" might outweigh the experience. The rest of the significant associations were all related only to the self-perceived outcome. Gardening group members who obtain more social capital (help, positive feedback and networking) over the summer feel that they receive more outcomes, similarly to earlier studies related to community gardens where longer collective action as a positive outcome correlates strongly with social cohesion and trust 43 . The finding emphasizes the social importance of the activity, which may be generalized to a wider natural resource governance 53 .Gardeners who worry about damage such as vandalism, theft or animal damages happening to their cultivations (worries) evaluate to receive less from the activity, as assumed. The variable was placed under the "past experiences" of the actors sub-system but it could be also related to the "mental models and knowledge of SES" 3 . The worries were stated at the beginning of summer, meaning that they do not necessarily associate with actual experiences but rather with gardeners` negative attitudes. The open and public location can create uncertainty related to risks and gardeners` control, which influences the outcomes 44 .
We found that the sunnier place the box was located in, the more self-perceived outcome was received. It was the only significant predictor from a SES framework sub-system resource, and, associated with the productivity of the system (RS5) 3 . Previously it has been found that the size of the resource system i.e. garden size or box number in our case strongly influences plant species richness, which was not found in our study 38 . Taken together, our analyses suggest that SES framework variables mainly related to the level of the individuals cooperating in governing the resource (actors) are of importance in our urban gardening system, especially in terms of self-perceived outcomes.
We were unable to find many associations between the ecological outcome and our predictor variables, which indicates low importance of the physical harvest as a motivator, supporting previous findings 43 . We also found that variables from governance subsystem, involvement indicating the fair division of labor, and rules were not significant predictors, contrary to many other natural resource systems 15 . However, in community gardens . The SEM results for the variables belonging to the sub-systems Actors, Governance, Resource and Evolutionary theory, predicting the two latent variables Self-perceived and Ecological outcomes described by their reflective indicators. The regression coefficients presented by arrows pointing to the latent variables show the significant (p value < 0.05) associations between the predictors and the outcomes (note that the non-significant predictors were not omitted from the model, see Table 2). The estimates presented are unstandardized estimates and their standard errors are presented in brackets. Error terms signifying the variance not explained by the model are included for latent variables and the reflective indicators. www.nature.com/scientificreports/ monitoring and sanctions are not assumed to be important as free-riding in the form of the physical resource is not perceived so negatively because of the low importance of the harvest 43 . Less than 40 % of variance in ecological outcome was explained in our models while for the self-perceived outcome the number was over 80 %. Therefore, we encourage future studies to include additional predictors to reach better understanding of the aspects mediating ecological outcomes 13,32,38 . The literature on urban gardening is largely based on community gardens and domestic gardens, and these kinds of urban gardens are markedly different from garden boxes. One clear difference is that community and domestic gardens are organized and governed in a different way, and when different motivations drive the participants, the dynamics also change 14 .
In previous studies factors such as gender, region of origin, neighborhood, motivations and time spent gardening have been found to influence changes in plant species diversity 32,38 . Our findings are partly based on questionnaire data, where the non-respondents can differ from the observed respondents. For example, nonrespondents can be gardeners not experiencing positive outcomes, and their exclusion could weaken the links between the predictors and outcomes. The garden box scheme, run by the City of Turku, collects no personal information and we therefore lack background knowledge on the profile of urban gardeners in this scheme. Our Table 2. SEM Results for the Structural Model (Fig. 3). This table presents the unstandardized estimates for the regression coefficients, their standard error and p value for all the independent variables predicting each latent outcome variable in the urban gardening system. The significant values (p < 0.05) are in bold. They signify a meaningful predicting power of the independent variable on the latent variable when including all the other variables and the covariances between the independent variables in the model. www.nature.com/scientificreports/ survey was distributed in multiple ways contacting all the gardeners (directly to registered users, social media and by leaflets placed at the garden boxes); we achieved a high response rate of about 50% 54,55 . Arguably, this high response rate safeguards the findings from strong biases due to non-responsiveness. However, the possible bias toward overrepresentation of the successful respondents prevent us from making clear conclusions about why and when gardeners fail entirely in this activity. Clearly, however, subsequent studies of gardening box systems would benefit from including more socio-demographic characteristics 38 .
Our third study question considered if the variables relatedness, stability of groups or repetition of interactions, derived from evolutionary theory would be relevant in our study system 22,23 . None of them were found to associate with the ecological outcome, but we were able to show that more frequent interactions significantly influence positively the self-perceived outcome. Relatedness, an important aspect explaining cooperative behavior in non-human world, is thus not notably significant when controlled by stability and group meetings 4 . However, in line with other studies showing how indirect fitness benefits drive cooperation in humans 20,21 more selfperceived social, individual-level and ecological benefits were received in groups where members interact more frequently with each other. Furthermore, as emotions and other psychological mechanisms seem to mediate human cooperation in many contexts, it is possible that self-perceived benefits, even if dissociated from biological fitness, could foster sustainable resource use in many SESs 56 . The presence of face-to-face communication is known to be an important variable in forming sustainable resource governance 5 and repeated interactions increase collective action in community gardens 2,43 . When group members meet more often, it can improve mutual trust, division of labor and efficiency facilitating collective action 24,25 . There`s also more opportunity for social control, which eventually leads to the correlation of strategies within groups and makes the actors more cooperative 4 . Due to the high importance of face-to-face communication in literature and our finding being in line with other studies, we can suggest that frequent interactions is a major indicator for working natural resource governance 25,57 .

Conclusions
Our findings suggest that the decoupling of ecological and self-perceived outcomes stems from the aspect that they mainly are impacted by different variables. Due to limited scope of our study, we note that further work in similar systems is needed to establish the finding and the causal linkages. However, a combination of selfevaluated as well as objectively measured outcomes seems relevant in analyzes of natural resource governance. In particular in urban gardening projects, where both social and ecological resilience of cities is a key aim, the disconnection highlights the need for more ecological awareness 13,37 .Although urban garden boxes have only a small effect on urban resilience, their cumulative local influence can be higher through well-working spatial and temporal coordination 13 . Our results both have practical value for urban commons governance, and contribute theoretically to SES research by highlighting perspectives from evolutionary explanations of cooperation 4 . Even if slightly limited by the small sample size, we were able to model the self-perceived and ecological outcomes of the activity as latent variables including multiple measures, which has a great advantage when comparing different systems and case studies 19,35,46 . Our results emphasize the social importance of the activity, and highlight the importance of frequent interactions to positive outcomes in natural resource governance 24,25,57 . Diminishing outcomes with time suggest it's important to carry out long term studies in order to understand the motivations of actors and their effects on the ecological and social impacts. Despite their differential effects, the variables we here identify correlating with outcomes are mostly aspects pertaining to the actors in the system. We, therefore, believe our findings exemplify the importance of understanding natural resource governance systems at a very low "grassroot" level.

Methods
Urban garden boxes in the public space. This study was conducted in 2019 in the urban area of a medium-sized city of Turku (population about 200 000) in Southwestern Finland and focused on a group of urban box gardeners enrolled in the city`s gardening program. The city provides one or more garden boxes (each 1 m 2 in size) and soil for free for people who volunteer to take care of them. The gardeners self-organize, can cultivate whatever they desire and the boxes are placed where the gardeners choose as long as they are on public land. Each year the demand exceeds the supply as the city distributes only a limited number of boxes. In 2019 there were 664 garden boxes in 228 different locations (Fig. 5). The boxes were located widely around Turku area, however mainly in the city center.
Modifying the SES framework for urban garden boxes. First, we considered which variables in the second-tier variable list of the SES framework 3,15 are potentially relevant to urban gardening outcomes (Table 1;  a complete list see Supplementary Table S1). The variables of the framework are not all intended to be used in every case study 18 : the addition or exclusion of the variables as well as their explicit operationalization depends on the context. We were especially interested in actors directly involved in resource governance, in their decision making and local conditions for resource sustainability. To this end, nine SES variables and three evolutionary variables were chosen to predict nine outcomes. We based our data collection on this selection. Some of the SES variables were operationalized by one measured variable (e.g. size of the resource system = box number), while some were operationalized by a higher number of measured variables (e.g. number of relevant actors = group size and others number). Data collection. Data was collected by field inventories and two questionnaires sent to the gardeners in summer 2019. The field inventories aimed to collect variables objectively measuring the ecological outcome and the SES resource sub-system. The field data was collected from all of the urban gardening boxes (664) (228) in the Turku area. The garden boxes were inspected three times five weeks apart (June, July and September). The average values per box over the summer are used in the analyses. During each visit, to assess the ecological outcome, the cultivated species were identified and counted, their quality and area cover were evaluated and the area covered by weeds was estimated (Table 1). In addition, the garden box location was evaluated for the average shade, privacy, and possible damage to the cultivations or boxes (Resource system, Table 1). Extra effort (RS4 human-constructed facilities) was recorded for the group if any kind of additional effort was observed, as this was seen as a sign of motivation 32 .
To elaborate the economic benefits of gardening, the estimated economic value of cultivations per box was included as one measure of the ecological outcome. While this is atypical in SES research, it is an additional aspect of gardening success. After each field inventory, an approximate sales price (€) for buying the gardened product in a shop in Turku (foodie.fi, 2019) was computed. The price €/piece was calculated for each plant and the price €/kg was calculated for the species according to their area (m 2 ) and information acquired of the average yield kg/m 2 for each species 58 . In addition, the final economic value was multiplied by the quality of each species.
Two questionnaires were sent to the gardeners, one before and one after summer 2019, using an electronic questionnaire (made in Webropol 2.0 online surveys) (see Supplementary Table S2 & S3 online). All the enrollees were contacted through the city program`s gardener registry. Overall, 121 gardeners answered at least one survey, which was 53.1% of all the registered groups. The response rate is considered acceptable for representation (60 +/− 20 54 ) and the analyses were performed to these units 55 . As the boxes are applied by an electronic form, we can assume that an electronic questionnaire is accessible and that the gardeners have an equal chance of answering. We enhanced the response rate by advertising the survey in the program`s Facebook group as well as distributing a short information package at each box. There is no information considering the demographic attributes of all the enrollees, nor can we assume the gardeners to represent the attributes of the population of Finland or Turku in general. Therefore, a limitation for our study is the inability to investigate how the respondents differ from non-respondents in these aspects. As all the gardeners were approached and the response rate is high, we can assume that our data covers the gardener group sufficiently. In addition, there is no visible geographic bias in the representation of the respondents compared to the non-respondents and the questionnaire answers cover the areas where boxes are found (Fig. 5). In addition, the respondents represent adequately the starting years of all the groups (the proportional numbers: overall / survey in 2019: 39,47% / 35,83%, 2018: 21,49% / 25,83%, 2017: 15,79% / 10,83% and 2016: 23,25% / 27,50%).
The questionnaires collected data to measure the two variables belonging to the subsystem governance (rules, involvement), six variables belonging to the subsystem actors (group size, others number, starting year, damage, worries, social capital), three variables belonging to the subsystem evolutionary theory (group meetings, relatedness, stability) and three variables measuring self-perceived outcome (social, individual and ecological benefits) (see all questions Tables S2 & S3 online, all variable definitions Table 1). Next, we describe some variables that may need further clarification. The relatedness was estimated as the respondent`s description of their family connections in the group. They stated if people in their gardening group were their family members (children and/or parents), other family members, friends, neighbors, or others. The social capital was formed as a composite consisting of questions about reciprocity, feedback and social networks related to the activity 25,53 . The after-summer questionnaire asked about 14 different benefits potentially obtained from the garden box activity to measure the self-perceived outcome. This list of benefits was partly based on the self-identified expectations from the survey before the summer, and partly on previous research 26,31,33 . The respondents were asked if they received these benefits during the summer and hence constituted a self-evaluation of the outcomes. 12 of the benefits were grouped into 3 categories depending on if they were related to individual, social or ecological benefits. To have 4 in each category, overall happiness (not possible to group under one category) and new acquaintances (not an expected benefit) were excluded from the analysis. The benefits were not studied separately due to the limitation of our small sample size. www.nature.com/scientificreports/ The information collected through the field inventories was connected to the information collected from the surveys by a name the group had stated for themselves when registering to the city. The surveys were planned for gardening groups, but some respondents reported taking care of the boxes alone. There were questions (rules, involvement, group meetings, relatedness and stability), which could not be answered sensibly by a one-person group, and therefore these answers had to be excluded from these questions (NA).
Modeling the urban gardening resource system using structural equation modeling. Structural equation modeling (SEM) combines factor analysis and path analysis into a single statistical framework 31 . The main advantage of SEM is the possibility to construct multiple-indicator latent (unobserved) constructs that represent constructs of scientific interest while accounting for measurement error. Our analyses were primarily based on an a priori hypothesized but simplified social-ecological framework (Fig. 1). First, we applied confirmatory factor analysis (CFA) to construct a measurement model with ecological and self-perceived outcomes as latent variables, each measured by reflective indicators (i.e., indicators are assumed to be causally affected by the underlying latent variable) 45 . The ecological outcome in the urban garden boxes was measured by six indicators recorded during the field inventories; the number of species per box (the marker variable used to scale the latent variable by fixing its loading to 1 and intercept to zero), number of cultivations per box, area of cultivations per box, average quality, average economic value and coverage of weeds per box ( Table 1). The number of cultivations was divided by 100 and coverage of weeds and economic value were divided by 10 to avoid too large unique variances of the indicators. The self-perceived outcome of garden box activity was measured by three indicators quantified in the questionnaire; i.e. social benefits (the marker variable), individual benefits and ecological benefits ( Table 1). All these indicators were continuous variables ( Table 3). The indicators measuring each latent variable correlated with each other (Tables 4 and 5), as required for reflective indicators assumed to be causally linked with the same latent 59 . To compare the indicators` relative differences the fully standardized parameter estimates for the factor loadings were reported.
The two latent variables were modelled simultaneously to investigate their association. The global fit of this model to the data was evaluated by a chi-square test and the following fit indices: root mean squared error of approximation (RMSEA) and comparative fit index (CFI) 48 . In the chi-square test, the p value over 0.05 signifies acceptable model fit, since the null hypothesis is testing whether the model-implied variance-covariance matrix equals that of the observed data. The cut-off values of fit indices for an acceptable model fit are for RMSEA =< 0.06 and CFI > 0.90 48 . The models for small sample sizes can be over-rejected and therefore we used the Swain`s correction factor (in this study = 0.965) to evaluate model fit using the R function swain.
Second, in the same framework, we regressed the variables from the actors, governance, resource, and evolutionary theory subsystems on the two latent variables, self-perceived and ecological outcomes to investigate which of the individual variables would statistically predict the outcomes. Most of the predictor variables were coded as binary for the analysis, except for two ordinal and four continuous variables, which in the analyses are both treated as continuous ( Table 3). The variables regressed to the latent variables did not present significant correlations with each other, showing that multicollinearity was not an issue here (Table S4 online) 59 . The global model fit indices are not available for the second model due to multiple imputations to handle missing values (see below 49 ).
Our data contained non-normal continuous response variables (i.e. indicators), and therefore we used a robust maximum-likelihood estimator (MLR) 49 . Our sample size (n = 121) is relatively small for SEM analysis, which can cause convergence issues and bias in parameter estimates 50 . The rule of thumb for a sufficient sample size of 10 observations per 1 free parameter was not realized for the measurement model (114:28) or the second model (114:58) 45,60 .However, it has been found that a small sample size might not face these issues when factors are defined by 3 or more indicators, 5 or fewer latent variables are created and an ML estimation is utilized 61,62 . In addition, when the model converges within a small number of iterations (max 50) and parameter estimates are reasonable, including relatively small standard errors, the results for local parameter estimates are not biased owing to a small sample size 50 . In this study, all of the above-mentioned requirements were fulfilled.
The CFA model excluded 7 observations as they contained missing data in all of the variables. Missing data for independent variables in the second model was dealt by multiple imputation (MI) 49 . In MI, multiply imputed datasets are created where the missing values are substituted, analyses are performed for each dataset and the results are combined. The main advantage of MI is to account for the uncertainty of estimating missing data by considering the variability between the datasets. To assure the reliability of the results (point estimates and their SEs) in the presence of over 60% missing data in some variables and maintain statistical power for our sample size, 100 imputed datasets were generated for our analyses 63 . MI can be used to obtain reliable results for nonnormal data, small sample size as well as high proportions of missing data 64 . The missing values for indicators (treated as dependent variables in all models) were not imputed in the datasets, but the model was estimated for each imputed dataset using full information maximum likelihood (FIML) 65 . Analyses were conducted using Mplus (Version 8.5) 49 . Mplus code for performing the MI and models are provided in the supplementary material (Fig. S1a-c. online).
Ethical approval. This study was conducted by the University of Turku. It collected opinions from human participants in a garden box scheme operated by the City of Turku by means of a questionnaire amongst garden box participants. Participation in the study was voluntary. A link to the survey was sent out to participants directly by the City of Turku without involvement of the University of Turku. In addition, links to the survey was distributed via social media and was advertised as a flyer left anonymously on the garden boxes. The questionnaire did not contain questions allowing identification of individuals. As a consequence, the information for this study was gathered in a manner where no personal information was collected by the University of Turku  15 November 1991). The study protocol and data management are all in accordance with the EU General Data Protection Regulation (GDPR) principles. All participants were provided with the required information about the project, data protection and participant rights through a GDBR-compliant privacy notice. Informed consent was obtained from all participants when they submitted the information and agreed to participate in the project. The responding to the questionnaire is considered to be written informed consent as the respondents were fully informed by the privacy notice and the questionnaire did not collect any personal information nor include sensitive questions. The data provided can be used for publication. Given our study followed the above outlined criteria, no ethical review is needed according to the Finnish ethical guide- Table 3. Descriptive statistics for the variables used in the analyses. This table reports descriptive statistics on the outcome and predictor variables. The data for the 121 gardening groups consists of information from different sources (field, two questionnaires), which leads to varying amount of missing values reported here. The variables were treated in the analyses as continuous or binary. See the description for each variable in Table 2.

Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.